The last example on the page is a much better illustration of non sequitur: "If I wear my new shirt, all the girls will think I'm sexy." A non sequitur is more like making up a syllogism with no basis for the initial statement.

So let p="I wear my new shirt", and q="all the girls think I'm sexy". The syllogism is

If p then q

p

therefore q

The syllogism is valid, but the first statement is unsupported.

Likewise, "If there were no God, there wouldn't be flowers." That's another non sequitur.

...is a form of non sequitur, as is its counterpart, denying the antecedent...

If p then q

not p

therefore, not q

These arguments are both invalid because the conclusion "does not logically follow" from the premises, thus, non sequitur. All logical fallacies are, technically, non sequiturs.

I think what you're referring to might be considered a sort of informal non sequitur but, in reality, it is simply an objection to the soundness of the argument. Your example...

If p then q

p

therefore q

Is valid, as you pointed out, but what you're really doing is declaring that the premise of a specific example of the argument is unsound (If I wear my new shirt then all the girls think I'm sexy). As an argument is sound only as long as it is valid and the premises are true, your objection is that the premise is false and that the argument is unsound.

I'm not positive, but I'm pretty sure that every logical fallacy relates to validity only, and not soundness. Objections to soundness go to the factual nature of the premises and not structure....but I'm going to have to dig a bit deeper to be sure.

The article still needs a rewrite, for clarity and a bit more depth.- Sans Deity 12:00, 31 August 2006 (MST)

I did a ton of research last night and I'm still putting it together, it seems that working up the various logic sections is going to be my next major project. What I've discovered is that the idea above (see strike-through) is correct but imprecise. I'll try to get some reworking done for the logical fallacies and non sequitur articles soon. -- Sans Deity 08:12, 1 September 2006 (MST)